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The aim is to establish the Finite-Resolution Persistence Theorem and understand its implications in various systems.

January 18, 2026Open Access

The Finite-Resolution Persistence Theorem (FRPT)

Key Points

The aim is to establish the Finite-Resolution Persistence Theorem and understand its implications in various systems.
Formulated the Finite-Resolution Persistence Theorem (FRPT) based on resolution capacity.
Analyzed the behavior of systems when input variation surpasses local resolution capacity.
Unified insights across computational, physical, and informational domains.
Identified that unresolved residue accumulates when input variation exceeds resolution capacity.
Demonstrated that these accumulations manifest as anomalies in system behavior.

Abstract

We present the Finite-Resolution Persistence Theorem (FRPT), a fundamental constraint governing systems operating under finite resolution capacity. The theorem establishes that when input variation exceeds local resolution capacity (χ > 1), unresolved residue must accumulate and persist, manifesting as observable anomalies in system behavior. This framework unifies phenomena across computational, physical, and informational domains through a resolution-based lens.

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C. James Kruse

Texas Department of Transportation

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The Finite-Resolution Persistence Theorem (FRPT)

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Abstract

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